Mustapha Ishak- Cosmic Acceleration: A procedure to distinguish between dark energy models and modified gravity models

8/3/2019 Mustapha Ishak- Cosmic Acceleration: A procedure to distinguish between dark energy models and modified gravity models

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Mustapha Ishak (U.T. Dallas) 1

Cosmic Acceleration:A procedure to distinguish between darkenergy models and modified gravity

models

Prof. Mustapha Ishak

Cosmology and Relativity Group

Department of Physics

The University of Texas at Dallas

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Cosmology & Relativity at

University of Texas at Dallas


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References and collaborators:

Probing Cosmic Acceleration Beyond the Equation ofState: Distinguishingbetween DarkEnergy and Modified Gravity ModelsMI, Amol Upadhye, and David Spergel, Phys.Rev. D74 (2006) 043513, astro-ph/0507184 (2005)

"Dynamical darkenergy: Current constraints and forecasts"Amol Upadhye,MI, Paul J. Steinhardt

Physical Review D, 72, 063501 (2005). astro-ph/0411803.

"Probing decisive answers to darkenergy questions from cosmic complementarity and lensing tomography"MI, Monthly Notices ofthe Royal Astronomical Society, V363, issue 2, p469 (2005). astro-ph/0501594

Remarks on the formulation ofthe cosmological constant/darkenergy problemsMI (2005). astro-ph/0504416

Why is the cosmic expansion accelerating? A shared obsession


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A comment : We should keep the constant- inthe inventory of possible solutions

to cosmic acceleration

Weyl, Cartan, and Lovelock showed different theorems that themost general curvature Einstein tensor is given by

Spacetime can have an intrinsic curvature without the need foran energy-momentum tensor justification

This is important to consider because:

1) It reopens the door to the search for perfect cancellationmechanisms for vacuum energy

2) Or also how vacuum energy gravitates?

3) Not anymore necessary to justify the value or the sign of theobserved

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What kind of answers are we going to be able to provide fromthe Dark Energy equation of state approach?

The most decisive answer will be if the data can show conclusively thatDark Energy is not a cosmological constant

It will be possible from several combinations of experiments to excludesome proposed models, trackers or some SUGRA inspired models withfor w0=-0.8 and w1=0.3

A very suggestive but less decisive answer will be to show that theDark Energy parameters are those of a cosmological constant to a veryhigh level of precision (a few percent?)

In all cases, a burning question is to know if what is obtained from thedata is the equation of state of some dark energy cosmic fluid or a justa result obtained because we tried to force a dark energy model on thetop of a modified gravity model?


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Probing cosmic acceleration beyond theequation of state: or also going further

using the equations of state Cosmic acceleration can be caused by:

1) An energy component in universe (e.g. dark energy, vacuum energy) 2) A modification to gravity at cosmological scales e.g. DGP, or higher-order invariants theories, or other MG models

An important step will be to distinguish between the 2 causes above: i.e. darkenergy or modified gravity

We were not interested in a particular model of modified gravity but ratherinterested in the ability to distinguish if we are in presence of one cause or theother.

The procedure will also answer the question of true or forced equation of state

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DETF final report: section III 2a) on page 7.


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Basic idea of the approach The cosmic acceleration affects cosmology in two ways:

1) It effects the expansion history of the universe 2) It effects the growth rate of large scale structure in the universe (the rate at which clusters and super

clusters of galaxies forms over the history of the universe)

The idea explored is that, for dark energy models, these two effects must be consistent one withanother because they are mathematically related by General Relativity equations

The idea has been discussed by our group and others groups as well (e.g. Lue, Scoccimarro, andStarkman,2004; Song 2005; MI, Upadhye, and Spergel 2005, Knox, Song, and Tyson, 2005) butthe challenge was to implement it using cosmological probes

We proposed a procedure to do that where the key step was to compare constraints on theexpansion and the growth using different and specific pairs of cosmological probes in order to

detect inconsistencies (MI, Upadhye, and Spergel, Phys.Rev. D74 (2006) 043513 , astro-ph/0507184)

The presence of significant inconsistencies between the expansion history and the growth ratecould be the indication of some problems with the underlying gravity theory

The proposed procedure detects such inconsistencies when they are present as we show


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Dark Energy models considered: the ones most

commonly used in papers

The equation of state of a cosmic dark fluid:

Negative w < -1/3 gives an accelerating expansion

Two levels of difficulty:

1) A constant EOS w.2) A variable EOS w(z)

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An example of modified gravity at cosmologicalscales: The Dvali, Gabadadze and Poratti model

(DGP model, 2000). The action for this 5-dimentional theory is given by

The idea is that our universe is a brane embedded in a 5D bulk

The first term describes the bulk while the 2 others are the usual 4D ones

The 2 different pre-factors in front of the bulk and the brane actions give rise to a characteristic lengthscale rc

At distance scales much smaller than this characteristic distance, we have the usual gravitational physics;On scales larger then rc, the full 5D physics is recovered

The result is that gravity is weakened at scales comparable to rc and the effect of the bulk causes cosmicacceleration.

Some of these models are consistent with current cosmological data and is a good example to use to testthe proposed procedure (note: we are not particularly interested in the viability of this model but only inusing it as an example to illustrate the procedure)


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The consistency relation between the expansionhistory and the growth rate of large scale structure

For the standard FLRW model with k=0 and a Dark Energy component, the expansion history is expressed by the Hubble function and is given by

And the growth rate G(a=1/(1+z)) is given by integrating the ODE:

For Modified Gravity DGP models and k=0, the expansion history is given by

And the growth rate of function is given by

Equation (1) and (2) must be mathematically consistent one with another via General Relativity. Similarly, equation (3) and (4) must be consistentone with another via DGP theory

Our approach uses cosmological probes in order to detect inconsistencies between equations (1) and (2).

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The SN luminosity-distance, theexpansion history, and Dark Energy

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Dark Energy versus DGP model Hubble

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Supernova Hubble diagrams for several darkenergy and DGP models. Note that the LCDMmodel (red solid line) and the m=0.20 DGPmodel (blue dotted) have nearly identical Hubblediagrams, but different growth factors as shown inFig. 1b. The same is true of the SUGRA (greendashed) and m =0.27 DGP (black double dotted)models.

Growth factor of linear density perturbations forseveral dark energy and DGP models. Note thatthe growth factor in the m=0.27 DGP model issuppressed with respect to that in the LCDMmodel, which has the same m.


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Weak gravitational lensing information is

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Weak lensing captures the effectofDarkEnergy on the expansion

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Convergence Power Spectrum


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Tomography auto power spectraand the cross-correlation for 2 redshift bins (it should be possible to

do about 10 bins with the bestproposed future experiments)

A promising technique ofweak lensing is called

tomography: it requires

dividing the source galaxies

into intervals of red shift

called tomography bins

Cosmic shear tomography


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The Cosmological Experiments simulated

We used 2000 supernovae with maximum redshift1.7 (and included some of the systematic limits)

A weak gravitational survey covering 10% of thesky (we also included some systematic limits)

10 weak lensing tomography bins

CMB experiment: 1 year of data from PLANCK


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Procedure proposed to find an

inconsistency: A first basic check Assume that the true universe is described by a modified gravity model (for example, we used the DGP

model).

So in this case, the true expansion history and growth rate functions are those of a DGP model.

However, assume that the cosmological data are analyzed using dark energy models instead

Determine the effective Dark Energy model from the best fit to measurements of the expansion history

This gives a first effective Dark Energy parameter space I:

Determine the effective Dark Energy model from the best fit to measurements of the growth ratefunction

This gives a second effective Dark Energy parameter space II

Compare the two effective parameter spaces to look for inconsistencies

A significant inconsistency between the dark energy parameter spaces will be a signature of theunderlying modified gravity model

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A first pedagogical example, and it

works! The inconsistency shows up


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Implementing the procedure using simulatedcosmological observations form near future experiments

SN+CMB versus WL+CMB

We assume that the true cosmology is that of modified gravity DGP model and generateSupernova magnitudes, Weak Lensing convergence power spectrum, and CMB temperaturepower spectrum.

We determine the effective Dark Energy model from the best fit to the supernove data andthe CMB power spectrum (we use pairs including the CMB in order to break degeneraciesamong the model parameters). The pair [Supernova+CMB] probes the expansion history

This gives a first effective Dark Energy parameter space I: e.g.

We determine the effective Dark Energy model from the best fit to the weak lensingconvergence spectrum and the CMB power spectrum. The pair [Gravitational

Lensing+CMB] probes the growth.

This gives a second effective Dark Energy parameter space II

We compare the two effective dark energy parameter spaces to look for inconsistencieswithin the precision of the combinations of the cosmological probes used

A significant inconsistency between the dark energy parameter spaces will be a signature ofthe underlying modified gravity model

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The significant difference (inconsistency) between the equations of state found using

these two combinations is a due to the DGP model and should be detectable by future

experiments.

In this simulated case, The inconsistency tells us that we are in presence of modified

gravity rather than GR+dark energy.

Results: Equations of state found using two different combinations of simulated datasets. Solid contours are for fits to the [Supernova + CMB] data combination, whiledashed contours are for fits to [Weak Lensing + CMB] data combination.(MI, Upadhye, and Spergel, Phys.Rev. D74 (2006) 043513 , astro-ph/0507184)


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Distinguishing dark energy and modified gravity hasnow generated a lot of discussion and work in the field:

Also Robert Caldwell, Asantha Cooray, Alessandro Melchiorri, Mars 2007; KazuhiroYamamoto, David Parkinson, Takashi Hamana, Robert C. Nichol, Yasushi Suto, April2007; and others

Sheng Wang, Lam Hui, Morgan May, Zoltan Haiman, May 2007) where they applied thesame method we proposed but using some current data and and w instead.


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Discussion, conclusion, and

future work The observed inconsistency in the figure is a consequence of our hypothesis that the true

cosmological model is a modified gravity DGP model.

Thus, the inconsistency constitute an observational detection of the assumed underlying modifiedgravity model or simply of problems with the underlying gravity theory

Note that we dont need to know the underlying model in order to detect any problems with thecurrent used theory

Finding two significantly different equations of state implies that these are not true EOSs butforced ones

Future work is needed in order to sharpen the test proposed, e.g.: To consider other dark energy models (with couplings, unusual sound speeds), To consider other modified gravity models in order to study the form of the inconsistencies To compare with inconsistencies due systematic effects in different data sets

The procedure is based on the comparison of measurements of the expansion history andmeasurements of the growth rate of large scale structure and shows that we can go beyond theequation of state analysis.

The procedure allows one to distinguish between some dark energy and modified gravity models.

Being able to distinguish between the two possibilities is and important step in the quest tounderstand cosmic acceleration


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In a golden eraofcosmology, We knowa lot

aboutouruniverse butwe understand very little

Contents of the universe:

Baryons: 4%

Darkmatter: 23%

Darkenergy: 73%

Massive neutrinos:0.1%

Spatial curvature:very close to0


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Weak gravitational lensing

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sources->


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Mustapha Ishak- Cosmic Acceleration: A procedure to distinguish between dark energy models and modified gravity models